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In this paper we consider the problem of computing generalized eigenvectorsof a matrix pencil in real Schur form. In exact arithmetic, this problem can besolved using substitution. In practice, substitution is vulnerable tofloating-point overflow. The robust solvers xTGEVC in LAPACK prevent overflowby dynamically scaling the eigenvectors. These subroutines are sequentialscalar codes which compute the eigenvectors one by one. In this paper wediscuss how to derive robust blocked algorithms. The new StarNEig librarycontains a robust task-parallel solver Zazamoukh which runs on top of StarPU.Our numerical experiments show that Zazamoukh achieves a super-linear speedupcompared with DTGEVC for sufficiently large matrices.

Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils